Method for predicting seismic events

ABSTRACT

A method for predicting seismic events wherein measurable and calculable parameters relating to alterations in the shape of the geoid, such as centripetal and tidal gravitational effects, and gravitational anomalies related to a buildup of energy at any given point in the earth are incorporated with observations from at least two previous, subsequent seismic events, to calculate the energy buildup required to result in a future seismic event.

FIELD OF THE INVENTION

[0001] The present invention relates to methods of predicting theoccurrence of seismic events from changes in the earth's equipotentialgravitational surface due to polar motion. More particularly,accumulated gravitation shift in geoids between successive polar motionsis associated with the accumulation in energy in the earth's crust whichcan be correlated to seismic events.

BACKGROUND OF THE INVENTION

[0002] The majority and most destructive of earthquakes or seismicevents are the tectonic quakes which are a result of a sudden release ofenergy accompanying a shift or dislocation of the earth's crust(shallow) and in the upper mantle (deep).

[0003] Shifts in the earth's crust create a potential energy, which isoccasionally released in a seismic event. Due to the devastating resultsof earthquakes, particularly those occurring in populated areas, therehave been concerted efforts to predict such events.

[0004] There are known areas of frequent seismic activity such asgeological locations having faults. Monitoring stations are provided atthese locations which, at best, provide warning of an immediatelyimpending event. Monitoring primarily consists of recording geophysicalprecursors such as P-wave velocity, ground uplift, radon emission, rockelectrical resistivity and water level fluctuations. These precursorscan have lead times of one day through to several years depending uponthe magnitude of the upcoming event.

[0005] Some approaches to obtaining more advance notice or prediction offuture events includes statistical analysis of the history ofearthquakes in a given location so as to determine whether there is arecurrent, or cyclical pattern to the events. These methods can providea statistical value, for example, a 70% probability of an eventhappening every 100 years, but still leave an uncertainty of tens ofyears.

[0006] Generally however, there is a need for an earlier warning systemand one which can be tied to known and independent factors.

SUMMARY OF THE INVENTION

[0007] Using the motion of the earth's poles, a series of successivegeoids can be determined. The shift between incremental geoids providesinformation necessary to determine changes in gravitational anomaliesand ultimately the accumulation in energy at a given geologicallocation. Knowing the energy which was released in a previous seismicevent, the geoidal shift method of the present invention can be used tomonitor and predict a subsequent seismic event.

[0008] In a broad form of the invention, a method is provided forpredicting seismic events comprising: determining a first geoid surfaceat first instance in time; determining successive geoid surfaces forsuccessive and incremental instances in time; determining an incrementalenergy associated with each incremental shift between the successivegeoid surfaces; accumulating energy associated with the incrementalshifts; and comparing the accumulated energy with a pre-determinedenergy which has resulted in a seismic event as being indicative of thelikelihood of a future seismic event. Preferably, the pre-determinedenergy for a seismic event is determined by establishing measures of theenergy released in a previous seismic event.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009]FIG. 1 is a section through the center of the earth whichillustrates the effect of polar shift on the corresponding sectionthrough the geoid surface;

[0010]FIG. 2 is a section through the center of the earth whichillustrates the effect of polar shift on the forces at a geographicallocation on the earth;

[0011]FIG. 3 is a side view of a truncated ellipsoid earth illustratingrotational planes and rotation vectors of a single mass on the surfaceof a geoid;

[0012]FIG. 4 is a fanciful view to illustrate the tidal gravitationaleffects of the sun and the moon;

[0013]FIG. 5 is a plot of the polar motion of the earth over a selectedtime period of 1964-1968;

[0014]FIG. 6a illustrates two geoids spaced in time with partialindications of the many intermediate incremental geoids which could becalculated therebetween and the magnitude of the change in gravitationaleffect;

[0015]FIG. 6b is a pair of charts which respectively illustrate; a plotof the Δg over each time increment between two seismic events at t₁ andt_(n) and accumulates over time future event at t_(m), and a plot of theaccumulation of energy between events.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0016] It is not new that gravitational anomalies affect the shape ofthe equipotential surface of the earth. This undulating surface is alsoknown as a geoid. Effects which alter the shape of the geoid include thecentripetal effect of the earth's rotation (an equatorial bulge) andtidal gravitational effects. The surface undulates due to localgravitational anomalies. While the surface of the ocean provides a goodapproximation of the geoid, the shape of the geoid can also becalculated over a land mass. These undulations are conventionallydetermined as departures from the theoretical ellipsoid.

[0017] The geoid is associated with the earth's orientation which variesaccording to an annual elliptical component and a Chandler circularcomponent with a period of about 435 days. The variation is due in partto annual spring melt cycles and tidal effects which exert a torque onthe earth. This torque results in precession of the earth's rotationalaxis. The precession is not a steady process however, there beingdiscontinuities or a lull in the precession each time the tidal masscrosses the equatorial plane. Further, beyond the tidal precession, theearth itself undergoes a free, Eulerian precession, some times called a“free nutation” or the Chandler Wobble.

[0018] The earth's orientation or polar motion is monitored. One suchmonitoring service is the International Earth Rotation Service (IERS)located at the U.S. Naval Observatory. It has been determined that theearth's axis has scribed a conical path of about 23.5° in about 26,000years.

[0019] The major sources of energy for seismic events are thegravitational anomalies. Gravitational anomalies are generated bydifferences between the gravity equipotential surfaces and thecentripetal force of the earth's rotation (rω²). This value, of course,varies with latitude from zero at a pole to a maximum at the equator(r=Rcoφ). A shift in axis of the earth's rotation changes the radius ofrotation (a vector of rotation force is a component of the gravitationvector).

[0020] Variation of sea-level gravity from a theoretical ellipsoid wasfirst set forth, by mid-18^(th) century scientist Alexis Clairaut, as afunction of latitude. Adoption of internationally agreed upon constantsimproved the accuracy of the gravity calculations. Using the expressionfor gravity, relating mass and distance, increased distance from theearth's center can be added to the calculation. At sea level, thegradient is about −0.3086 milligal per meter of elevation increase.Calculations for such uniform changes in elevation are also known as theFree-Air Anomaly. Pierre Bouguer, again in the mid-18^(th) century, madecorrections for actual variations in topography. The resultingcorrection, about +0.20 milligal per meter of elevation increase, wastermed the Bouguer Anomaly. Further, there are well described variationsin the crust of the earth, known as the Mohorovicic discontinuities(Moho). Warping of these density interfaces also produce gravity at theearth's surface.

[0021] Suffice it to say that the geophysics for determining the geoidsurface are known and the detailed mathematics are not reproducedherein.

[0022] The equipotential surfaces, or geoids, change continuously overtime and certainly as a function of the polar motion. While this is acontinuous process, a series of incremental geoid surfaces can bedetermined from the empirical polar motion and tidal data.

[0023] The equipotential surfaces of the gravitation of successivegeoids intersect. A gravitational difference or shift Δg is representedby the difference between successive geoids. Maximum shifts Ag are alongthe meridian of shift. Minimums or zero Δg are found at intersectionpoints of the two equipotential gravitational surfaces.

[0024] Adjustments can be made to correct for delay in change of thehard body of the earth to compensate for the already changed rotationvectors.

[0025] The shift Δg can be expressed as a new surface over the earth.The Δg shift represents forces applied to the earth at that point. Thesurface of the Δg shift is calculated in incremental steps. Integrationof the Δg over time represents the accumulation of energy for the earthat that point.

[0026] Further, secondary energy sources include, listed according tomagnitude, the moon's tidal wave and the sun's tidal wave. Anothersource of unbalancing of the polar motion is the movements of the masseson the earth's surface by rivers and oceans.

[0027] The movements of the earth surface itself, such as mountaingrowth, can be a reaction to the gravitational anomalies and have thesame sign as the anomaly. The plastic Mohorovicic discontinuity moves tocompensate gravity to a stable position or to minimize the anomaly.Additionally, thermal effects of the Earth are as a result ofPressure-Temperature-Melting point drop function as described byBoyle-Mariotte's law.

[0028] The major horizontal earth movement energy in the earth isgenerated by coriolis force and a gravitational sliding or downwardmotion.

[0029] The movement of the earth's masses obeys the law of mechanics ofcontinuum where every material point has its own force field applicationand is not simply a hard, non-compressible body of flat form. Thesematerial point forces are integrated by the volume to obtain a largescale mass movement estimation.

[0030] Earthquakes or seismic events are known to be caused by thesudden release of energy within some limited region of the Earth. Theenergy is largely a result of an accumulation of elastic strain. Therelease of the elastic strain energy can produce major earthquakes.

[0031] By observing the point or region of the earth having twoconsecutive earthquakes in time, one can determine the energy requiredto cause the earthquake. This energy represents energy accumulated fromfactors including those caused by the shift of axis of the earth betweensaid events. From the known energy level, one can predict a similarenergy which will trigger or initiate a subsequent seismic event at thatsame location.

[0032] The energy due to polar motion can be estimated by summation ofthe incremental shift Δg at that location. Accordingly, by extrapolatingpolar motion and resulting shifts in geoid, one can predict the time ofthe next seismic event and its magnitude.

[0033] The theoretical determination of locations and forces involved inearthquakes can be obtained through mathematical modeling. Dependingupon the data available and the variables involved, the method varies incomplexity.

[0034] In one embodiment, a simplified general formula is developedwhich considers the energy sources, medium properties and geoidconfigurations. A mathematical formula is derived with its end useapplicable for computer-generated modeling.

[0035] Of all the possible energy sources, gravity and gravitation isconsidered to be dominant. Other secondary sources are divided betweenindependent sources such as the gravitational effects of the sun and themoon, solar radiant heat, and dependent sources involving thetransformation of energy such as pressure to heat, and others.

[0036] The earth's rotation, is considered to be the major variablesource and is subject to rapid change. Rotational energy is handled asan equation of the shape of the geoid and the present drift of thegeoid's axis of rotation. Between time t₁ and time t2, there will beincremental geoid surfaces gi and g₂. The shift Δg is the differencetherebetween, or

Δg=g ₁ −g ₂  (1)

[0037] Having reference to FIG. 4, one can see that the geoid rotationalsurface is defined by equal vectors of rotation. The motion of amaterial point is the dynamic earth's surface.

[0038] The known phenomena of drift of axis of rotation is defined as achange in position of an imaginary axis of symmetry of rotation of thematerial points where the radius is equal to zero.

[0039] During an earthquake, rapid movement of the earth's matter isgenerated. This displacement or movement Δh is working against theplastic properties of the earth at this point—the earthquake epicenter.As a result of a rapid strain release, the geological medium breaks, andthe energy released is in a shock-wave form.

[0040] The value of the function representing the energy generated isthe seismic energy. $\begin{matrix}{E_{q} = {{KF}_{k}\left( \frac{\Delta \quad h}{\Delta \quad t} \right)}} & (2)\end{matrix}$

[0041] where:

[0042] E_(q) is referred to as the energy generated,

[0043] F_(k) is the force,

[0044] K is the coefficient of the medium property, reflecting thechange of potential energy of tension to the dynamic energy ofrotation),

[0045] Δh—is the displacement or throw of the fault, and

[0046] Δt—is the time of duration of the movement or accumulated time inthe case of multiple shock events.

[0047] From the law of the preservation of energy, the energyaccumulated E_(a) equals the energy released E_(q).

E _(a) =E _(q)  (3)

[0048] This condition is satisfied when in the same geographical area,we have repeated earthquakes after known time interval T, where T isgreater than zero. (T>>0). Historically, one earthquake occurs at afirst instance in time t1 and a successive earthquake occurs at a secondinstance in time t2.

[0049] The total potential energy E_(p) is that energy accumulated inelapsed time T. After elapsed time T, following the seismic event, thepotential energy E_(p) is substantially zero due to the release duringthe earthquake. Smaller or minor earthquakes having energy E_(q0), maybe a result of residual accumulated energy of E_(a)−E_(q0). As is latershown, the potential energy is a measurable and calculable element. Fromthe known potential energy, we can find the total stress-force that isrequired to produce the earthquake.

[0050] Geological media properties A, which can be termed media propertyparameters, can be calculated using conventional methods ofdetermination such as drilling, seismic, gravity, etc. This gives onethe ability to adjust the solutions of systems of equations regardingone of the parameters.

[0051] One first models the earth's surface as a geoid surface and thegeoid as an ellipsoid of revolution. Now, assume that it is aplastically deformable body whose equipotential surfaces aresubstantially parallel to the geoid's surface. A graph of the model canbe simplified to that shown in FIGS. 2 and 3.

[0052] When, due to a shift in the axis of rotation, the equipotentialsurface of the gravitation V_(o), shifts to a position relative to thegravitated body of earth surface-geoid, the estimate of the value ofgravitation changes as ΔV.

ΔV=V ₁ −V ₂  (4)

[0053] where

[0054] V_(i) is the equipotential gravitation surface of the geoidbefore the shift of axis,

[0055] V′_(i) is the equipotential surface of the geoid after the shiftof axis,

[0056] V is the potential energy accumulated at this point on the geoid,and

[0057] ΔV is the difference between the new and the old equipotentiallevels.

[0058] Where the geoidal surfaces at t₁, and t₂ coincide, there is aminimal change in the trajectory of the earth's crust. Where the geoidalsurfaces vary, there is a gravitational anomaly and a shift in thevelocity vector or trajectory of the earth. This results in significantforces in the earth's crust.

[0059] At each point, there are two forces applied: {overscore (F)} dueto gravity and {overscore (K)} due to the centripetal force for{overscore (g)}={overscore (F)}+{fraction (K)}. The centripetal force isapplied in the plane of rotation and perpendicular to the axis ofrotation. Centripetal force can be represented as K=ω₂ρ where ρ is theradius of the plane of rotation and ω is the angular velocity.

[0060] In an ideal situation:

AV=kAg (5)

[0061] where Δg—is the gravitation anomaly generated.

[0062] But in practice the solutions are more complicated.

[0063] The IERS and others have precisely documented the polar motionfor more than 100 years. From this, we can obtain the accumulated valueof the total number of events, A, in a given area $\begin{matrix}{V_{a} = {\sum\limits_{i = 1}^{A}\quad {\Delta \quad V_{I}}}} & (6)\end{matrix}$

[0064] The limit of this value is $\begin{matrix}{V_{I} = {\underset{t\rightarrow\infty}{Lim}{\sum\limits_{i = 1}^{A}\quad {\Delta \quad V_{I}}}}} & (7)\end{matrix}$

[0065] The physical limit is reached when the potential (stress) energyis transformed into the dynamic (strain) energy and results in theearthquake. Therefore these two values are equalized at this time byequation. $\begin{matrix}{V_{I} = {f_{k}\left( \frac{\Delta \quad h}{\Delta \quad t} \right)}} & (8)\end{matrix}$

[0066] where f_(k) is a specific function which can be estimated.

[0067] One plots the equipotential surfaces of the ΔV on a geoidsurface. Overlaps indicate multiplication of Δg in this point and signala concentration of energy. As stated, using historical data for theenergy and the incident of the last earthquake event, the next may bepredicted.

[0068] Accordingly, by monitoring the accumulation of potentialgravitational energy E_(a) between two successive earthquakes at ageographical location and between times t1, and t_(n), and byextrapolating the ongoing accumulation of potential energy to somefuture polar motion at t_(m), we can predict the moment when theconditions are satisfied for a similar seismic event.

[0069] Having reference to FIG. 5, the polar motion for the period oftime between 1964 and 1968 are illustrated. It is hypothesized that abeat between the annual and the 14 month cycles results in theoccasional collapse or approach of the generally circular polar motion.

[0070] Turning to FIG. 6a, an exaggerated shift of the geoids over timedue to polar motion (P₁−P_(n)) illustrates how the net gravitationaleffects are increased in some areas and decreased in others. As shown atpoint Z, the effect is minimal at the intersection of the geoids. InFIG. 6b, the incremental changes in Δg for incremental instances in timet₁—t_(n) are plotted. At time t_(n), an earthquake event is indicated.By integrating Ag over time between t₁−t_(n), and applying theappropriate constants for determining energy, the energy E_(q) which wasnecessary to cause the earthquake at that particular locale can bedetermined.

[0071] Having V_(m) as an anomaly produced from periodic functions suchas moon gravity and sun gravity waves Δgm, the V₁ of Eqn. 8 can beadjusted.

[0072] Theoretical calculated values of Moon and Sun tidal gravitychange are:

[0073] for the moon, $\begin{matrix}{{\Delta \quad g_{c}} = {\frac{3}{2}{fM}_{c}\frac{\rho}{c_{c}^{3}}\left( \frac{c_{c}}{R_{c}} \right)^{3}\left\{ {\left( {{2\cos^{2}z_{c}} - \frac{2}{3}} \right) + {\frac{\rho}{c_{c}}\frac{c_{c}}{R_{c}}\left( {{5\cos^{3}z_{c}} - {3\cos \quad z_{c}}} \right)}} \right\}}} & (9)\end{matrix}$

[0074] and for the sun, $\begin{matrix}{{\Delta \quad g_{\oplus}} = {\frac{3}{2}{fM}_{c}\frac{\rho}{c_{c}^{3}}\frac{M_{\oplus}}{M_{c}}\frac{\sin^{3}\pi_{\oplus}}{\sin^{3}\pi_{c}}\frac{1}{r_{\oplus}^{3}}\left( {{2\cos^{2}z_{\oplus}} - \frac{2}{3}} \right)}} & (10)\end{matrix}$

[0075] where

[0076] Δg, Δg—first differentials on the Earth radius of tidal gravitypotential.

[0077] f—Gravity constant,

[0078] M_(c)—mass of Moon,

[0079] M_(⊕)—mass of Sun,

[0080] ρ=α(1−esin²ψ)−the distance from centre of earth to point ofmeasurement,

[0081] c_(c)−Average distance from centre of the earth to centre of themoon,

[0082] R_(c) the distance from centre of the earth to centre of the Moonon the moment of measurement,

[0083] r_(⊕)—the radius—vector of the sun.

[0084] sinπ_(c), sinπ_(⊕)the equatorial horizontal parallaxes of moonand sun,

[0085] z—momentary geocentric distance of moon and sun and

cosz−sinδsinψ+cosδcos ψcosτ  (11)

[0086] Where

[0087] δ—Latitude of the Moon or Sun,

[0088] τ—Hourly angle of the Sun and Moon

[0089] ψ—Geocentric latitude of the point of measurement.

[0090] The value of Δg is in range of hundreds of mgal compared to theaverage of the earth's gravity being 980 gal (1 gal=1 cm/s²).

[0091] The tidal correction can be made as follows: $\begin{matrix}{V_{I} \leq {{\sum\limits_{i = 1}^{A}\quad {\Delta \quad V_{I}}} + V_{m}}} & (9)\end{matrix}$

[0092] Through satisfying this condition, one is able to determine orpredict an earthquake event in time and place. Past experiments haveshown good correlation between seismic events and moon tide peaks.

[0093] There is a geological part of the methodology that is similarlydeterminable applying similar techniques. The vector calculus equationsthat actually define the gravity, gravitation and the elastic propertiesof the Earthquake, vector movements of a solid point of the geoid andcentripetal potential belong to the field of vector calculus and thetheory of the earth topography which are known to those of ordinaryskill in the art.

The embodiments of the invention for which and exclusive property orprivilege are claimed are defined as follows:
 1. A method for predictingseismic events comprising: (a) determining a first geoid surface atfirst instance in time; (b) determining successive geoid surfaces forsuccessive and incremental instances in time; (c) determining anincremental energy associated with each incremental shift between thesuccessive geoid surfaces; (d) accumulating energy associated with theincremental shifts; and (e) comparing the accumulated energy with apre-determined energy which has resulted in a seismic event as beingindicative of the likelihood of a future seismic event.
 2. The method ofclaim 1 wherein the pre-determined energy for a seismic event isdetermined by: (a) identifying a first instance in time when a seismicevent occurred at the geographical location; (b) identifying a secondinstance in time when a second successive seismic event occurred at thegeographical location; and (c) establishing measures of the energyreleased in the second successive seismic event.